Showing papers on "Radiative transfer published in 1994"

Light and Water: Radiative Transfer in Natural Waters

Abstract: Fundamentals: Radiometry. Photometry. Optical Properties of Water. Radiative Transfer: Across the Surface. Within the Water. Solutions Methods: Monte Carlo Methods. Invariant Imbedding Methods: Introduction. Invariant Imbedding Methods: Solving the RTE. Eigenmatrix Methods. Inverse Methods. Solutions: Underwater Light Fields. Epilogue. Chapter Problems. References.

Microwave Scattering and Emission Models and their Applications

Abstract: First-order radiative transfer solution first-order radiative transfer solution passive sensing formulation of the surface scattering problem surface model and special cases ranges validity of the IEM model matrix doubling formulations for scattering and emission scattering and emissions models for snow and sea ice comparisons of model predictions with backscattering and emission measurements from snow and ice.

Laser action in strongly scattering media

Abstract: THE radiative properties of an atomic or molecular system may be altered significantly in the presence of coherent optical scattering1,2. In the course of investigating the radiative properties of a laser dye dispersed in a strongly scattering medium (a colloidal suspension of titanium dioxide particles), we have found that the emissions from such systems can exhibit spectral and temporal properties characteristic of a multimode laser oscillator, even though the systems contain no external cavity. The threshold excitation energy for laser action is surprisingly low. We suggest that these composite systems might find applications in laser instrumentation and photonics.

Boundary conditions for the diffusion equation in radiative transfer

Abstract: Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80-100%, and a minimum value of 98% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, and we suggest a unified partial-current--extrapolated boundary approach.

Generalized comptonization models and application to the recent high-energy observations

Abstract: The theory of spectral formation in thermal X-ray sources, where the effects of Comptonization and Klein-Nishina corrections are important, is presented. Analytical expressions are obtained for the produced spectrum as a function of such input parameters as the plasma temperature, the optical depth of the plasma cloud and the injected soft photon spectrum. The analytical theory developed here takes into account the dependence of the scattering opacity on the photon energy. It is shown that the plasma temperature as well as the asymptotic rate of photon escape from the plasma cloud determine the shape of the upscattered hard tail in the emergent spectra, even in the case of very small optical depths. The escape distributions of photons are given for any optical depth of the plasma cloud and their asymptotic dependence for very small and large optical depths are examined. It is shown that this new generalized approach can fit spectra for a large variety of hard X-ray sources and determine the plasma temperature in the region of main energy release in Cyg X-1 and the Seyfert galaxy NGC 4151.

SMAC: a simplified method for the atmospheric correction of satellite measurements in the solar spectrum

Abstract: This paper describes a computationally fast and accurate technique for the atmospheric correction of satellite measurements in the solar spectrum. The main advantage of the method is that it is several hundred times faster than more detailed radiative transfer models like 5S and that it does not require precalculated look-up tables. The method is especially useful for correcting the huge amounts of data acquired by large-field-of-view high-repetitivity sensors, like the ones on board polar orbiting and geostationary meteorological satellites. The technique is based on a set of equations with coefficients which depend on the spectral band of the sensor. Semi-empirical formulations are used to describe the different interactions (absorption, scattering, etc.) of solar radiation with atmospheric constituents during its traverse through the atmosphere. Sensor specific coefficients of each equation are determined using a best fit technique against the computations of the 5S code (Simulation of Satelli...

On the hydrodynamic interaction of shock waves with interstellar clouds. 1: Nonradiative shocks in small clouds

Abstract: The interstellar medium (ISM) is inhomogeneous, with clouds of various temperatures and densities embedded in a tenuous intercloud medium. Shocks propagating through the ISM can ablate or destroy the clouds, at the same time significantly altering the properties of the intercloud medium. This paper presents a comprehensive numerical study of the simplest case of the interaction between a shock wave and a spherical cloud, in which the shock far from the cloud is steady and planar, and in which radiative losses, thermal conduction, magnetic fields, and gravitational forces are all neglected. As a result, the problem is completely specified by two numbers: the Mach number of the shock, M, and the ratio of the density of the cloud to that of the intercloud medium, Chi. For strong shocks we show that the dependence on M scales out, so the primary independent parameter is Chi. Variations from this simple case are also considered: the potential effect of radiative losses is assessed by calculations in which the ratio of specific heats in the cloud is 1.1 instead of 5/3; the effect of the initial shape of the cloud is studied by using a cylindrical cloud instead of a spherical one; and the role of the initial shock is determined by considering the case of a cloud embedded in a wind. Local adaptive mesh refinement techniques with a second-order, two-fluid, two-dimensional Godunov hydrodynamic scheme are used to address these problems, allowing heretofore unobtainable numerical resolution. Convergence studies to be described in a subsequent paper demonstrate that about 100 zones per cloud radius are needed for accurate results; previous calculations have generally used about a third of this number. The results of the calculations are analyzed in terms of global quantities which provide an overall description of te shocked cloud: the size and shape of the cloud, the mean density, the mean pressure, the mean velocity, the velocity dispersion, and the total circulation.

Stellar Interiors. Physical Principles, Structure, and Evolution.

Abstract: Preliminaries.- An Overview of Stellar Evolution.- Equations of State.- Radiative and Conductive Heat Transfer.- Heat Transfer by Convection.- Stellar Energy Sources.- Stellar Modeling.- Structure and Evolution of the Sun.- Structure and Evolution of White Dwarfs.- Asteroseismology.- Glossary.- Physical and Astronomical Constants.- Sample Computer Codes.- Index.

Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo

Abstract: We used simplifying assumptions to derive analytical formulae expressing the reflectance of shallow waters as a function of observation depth and of bottom depth and albedo. These formulae also involve two apparent optical properties of the water body: a mean diffise attenuation coefficient and a hypothetical reflectance which would be observed if the bottom was infinitely deep. The validity of these approximate formulae was tested by comparing their outputs with accurate solutions of the radiative transfer obtained under the same boundary conditions by Monte Carlo simulations. These approximations were also checked by comparing the reflectance spectra for varying bottom depths and compositions determined in coastal lagoons with those predicted by the formulae. These predictions were based on separate determinations of the spectral albedos of typical materials covering the floor, such as coral sand and various green or brown algae. The simple analytical expressions are accurate enough for most practical applications and also allow quantitative discussion of the limitations of remote-sensing techniques for bottom recognition and bathymetry. As early as 1944, Duntley used a spectrograph mounted in a glass-bottomed boat or flown in an airplane to analyze radiances emerging from the ocean and shallow waters. He evidenced the influence of the water depth on the spectral composition of the upward flux (Duntley 1963). Using a Monte Carlo technique, Plass and Kattawar (1972) calculated the radiative field in the atmosphere+cean system and in particular examined the dependence of the upward flux on the albedo of the ocean floor. Gordon and Brown (1974) studied the diffuse reflectance of a shallow ocean using Monte Carlo simulations and a probabilistic approach. Gordon and Brown provided an analysis based on photon history of the light field as modified by the presence of a reflecting bottom. In, addition, Ackleson and Klemas (1986) developed a two-flow model that simulated the light field within a canopy of bottom-adhering plants. A single scattering approximation for irradiance reflectance was also

Optical properties of pure water

Abstract: The optical properties of pure water are basic input data for many geophysical investigations such as remote sensing of surface water and underwater radiative transfer calculations. Knowledge of the spectral properties of components in surface water is required for accurate interpretation of measured reflection and attenuation spectra in terms of their concentrations. Also the sources and sizes of errors in the basic data must be known. Absorption measurements were done with a submersible absorption meter in the temperature range 2.5 till 40.5 degree(s)C. The scattering of pure water is recalculated using the Einstein-Smoluchowski equation. The input for this equation is evaluated and the temperature dependency is included. New values for the absorption coefficient are given based on these results and analysis of data from the literature. Absorption in the wavelength range 300 - 550 nm is lower than presently used values. In the wavelength range about 700 nm the spectrum has a different shape. A formulation of the effect of temperature on the absorption spectrum is given.

Effect of radiation trapping on fluorescence lifetime and emission cross section measurements in solid-state laser media.

Abstract: Radiation trapping causes significant lengthening of the measured fluorescence lifetime in optically thin solid-state laser gain media, which leads to underestimates of the stimulated emission cross section by as much as 30%. A measurement technique is demonstrated that greatly reduces radiation trapping in Yb:YAG, a prototypical quasi-three-level laser medium. The radiative lifetime of the (2)F(5/2) manifold was measured to be 0.951 ms at 300 K, which is more than 10% lower than any previous measurement. This more-accurate radiative lifetime gives a 1.03-microm peak effective stimulated emission cross section of 2.3 x 10(-20) cm(2). Our measurement technique is expected to be most relevant for three-level and quasi-three-level laser media.

Retrieval of sizes and total masses of particles in volcanic clouds using AVHRR bands 4 and 5

Abstract: The advanced very high resolution radiometer (AVHRR) sensor on polar orbiting NOAA satellites can discriminate between volcanic clouds and meteorological clouds using two-band data in the thermal infrared. This paper is aimed at developing a retrieval of the particle sizes, optical depth, and total masses of particles from AVHRR two-band data of volcanic clouds. Radiative transfer calculations are used with a semi-transparent cloud model that is based on assumptions of spherical particle shape, a homogeneous underlying surface, and a simple thin cloud parallel to the surface. The model is applied to observed AVHRR data from a 13-hour old drifting cloud from the August 19, 1992, eruption of Crater Peak/Spurr Volcano, Alaska. The AVHRR data fit in the range of results calculated by the model, which supports its credibility. According to the model results, the average of effective particle radius in the test frame of this cloud is in the range of 2 to 2.5 micrometer, the optical depth at 12 micrometer is about 0.60 - 0.65. The total estimated mass of ash in the air amounts to 0.24 - 0.31 x 10(exp 6) tons, which is about 0.7-0.9% of the mass measured in the ashfall blanket. Sensitivity tests show that the mass estimate is more sensitive to the assumed ash size distribution than it is to the ash composition.

Absorption and emission of light in nanoscale silicon structures.

Abstract: A unified model of phonon-assisted and zero-phonon radiative transitions in nanoscale silicon structures is presented. For characteristic sizes above 15--20 \AA{}, phonon-assisted transitions dominate, while zero-phonon transitions, allowed due to the finite-size effect, are more important for smaller length scales. Light emission from porous silicon is analyzed on the basis of these results showing that phonon-assisted transitions should dominate the emission in the observed red band.

A climate model study of indirect radiative forcing by anthropogenic sulphate aerosols

Abstract: ANTHROPOGENIC sulphate aerosols are believed to affect the radiation budget of the Earth in two ways. Through the direct effect they scatter solar radiation back to space, producing a radiative forcing whose global annual mean has been estimated to lie in the range −0.3 to −0.9 W m−2 (refs 1–3). This is significant compared to the longwave forcing due to increases in anthropogenic trace gases since the beginning of the industrial era, estimated at +2 to +2.5 W m−2 (ref. 4). Aerosols also have an indirect effect, altering the distribution and concentration of cloud condensation nuclei (CCN) and hence the number density and size distribution of cloud droplets, thus affecting the solar radiative characteristics of clouds5,6. This is harder to quantify than the direct effect, because it depends on complex and poorly understood interactions between aerosols, CCN and cloud properties. Here we use sulphate aerosol data derived from a three-dimensional chemical transport model7 to estimate the indirect radiative forcing by low-level water clouds using a general circulation model. We estimate that the indirect aerosol effect at the top of the atmosphere is approximately −1.3 W m−2 in the global annual mean. Although this value is subject to a high level of uncertainty, even if the effect is only half as large it would still exceed many estimates of the direct effect, demonstrating its potential importance in climate change.

Effect of precipitation on the albedo susceptibility of clouds in the marine boundary layer

Abstract: TROPOSPHERIC aerosols are thought to have three important effects on the Earth's radiation budget: the direct radiative effect1 (pertur-bation of clear-sky reflectivity), the indirect radiative effect2 (modi-fication of cloud albedo) and the effect on the hydrological cycle3 (modification of the vertical thickness and horizontal extent of clouds). The first two effects have been understood in principle for nearly 20 years, and quantitative estimates of their magnitudes have been provided by models and observations4. The third phe-nomenon, and its relation to the other two, has received far less attention. Previous work3 has shown, however, that increases in aerosol concentration may act to increase cloud albedo by increas-ing horizontal cloud fraction as well as cloud reflectivity. Here we use a simple model of the marine cloud-topped boundary layer to investigate the changes in cloud thickness and albedo that result from changes in precipitation as particle concentrations vary. We find that the sensitivity of layer cloud albedo to droplet number concentration (the albedo susceptibility) is increased by 50–200% when the dependence of cloud thickness on particle number is included. The results suggest that the response of cloud thickness to changes in aerosol particle concentration must be taken into account for accurate prediction of global albedo by climate models.

The optical properties of pure water

Abstract: The optical properties of pure water are basic input data for many geophysical investigations such as remote sensing of surface water and underwater radiative transfer calculations. Knowledge of the spectral properties of components in surface water is required for accurate interpretation ofmeasured reflection and attenuation spectra in terms oftheir concentrations. Also the sources and sizes of errors in the basic data must be known. Absorption measurements were done with a submersible absorption meter in the temperature range 2.5 till 40.5 °C. The scattering of pure water is recalculated using the Einstein-Smoluchowski equation. The input for this equation is evaluated and the temperature dependency is included. New values for the absorption coefficient are given based on these results and analysis of data from the literature. Absorption in the wavelength range 300-550 nm is lower than presently used values. In the wavelength range above 700 nm the spectrum has a different shape. A formulation of the effect of temperature on the absorption spectrum is given.

Nonaxisymmetric evolution in protostellar disks

Abstract: We present a two-dimensional, multigridded hydrodynamical simulation of the collapse of an axisymmetric, rotating, 1 solar mass protostellar cloud, which forms a resolved, hydrotastic disk. The code includes the effects of physical viscosity, radiative transfer and radiative acceleration but not magnetic fields. We examine how the disk is affected by the inclusion of turbulent viscosity by comparing a viscous simulation with an inviscid model evolved from the same initial conditions, and we derive a disk evolutionary timescale on the order of 300,000 years if alpha = 0.01. Effects arising from non-axisymmetric gravitational instabilities in the protostellar disk are followed with a three-dimensional SPH code, starting from the two-dimensional structure. We find that the disk is prone to a series of spiral instabilities with primary azimulthal mode number m = 1 and m = 2. The torques induced by these nonaxisymmetric structures elicit material transport of angular momentum and mass through the disk, readjusting the surface density profile toward more stable configurations. We present a series of analyses which characterize both the development and the likely source of the instabilities. We speculate that an evolving disk which maintains a minimum Toomre Q-value approximately 1.4 will have a total evolutionary span of several times 10(exp 5) years, comparable to, but somewhat shorter than the evolutionary timescale resulting from viscous turbulence alone. We compare the evolution resulting from nonaxisymmetric instabilities with solutions of a one-dimensional viscous diffusion equation applied to the initial surface density and temperature profile. We find that an effective alpha-value of 0.03 is a good fit to the results of the simulation. However, the effective alpha will depend on the minimum Q in the disk at the time the instability is activated. We argue that the major fraction of the transport characterized by the value of alpha is due to the action of gravitational torques, and does not arise from inherent viscosity within the smoothed particle hydrodynamics method.

Modelling radiation quantities and photolysis frequencies in the troposphere

Abstract: STAR (System for Transfer of Atmospheric Radiation) was developed to calculate accurately and efficiently the irradiance, the actinic flux, and the radiance in the troposphere. Additionally a very efficient calculation scheme to computer photolysis frequencies for 21 different gases was evolved. STAR includes representative data bases for atmospheric constituents, especially aerosol particles. With this model package a sensitivity study of the influence of different parameter on photolysis frequencies in particular of O3 to Singlet D oxygen atoms, of NO2, and of HCHO was performed. The results show the quantitative effects of the influence of the solar zenith angle, the ozone concentration and vertical profile, the aerosol particles, the surface albedo, the temperature, the pressure, the concentration of NO2, and different types of clouds on the photolysis frequencies.

Independent Pixel and Monte Carlo Estimates of Stratocumulus Albedo

Abstract: Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.

Solar Magnetic Fields: Polarized Radiation Diagnostics

Abstract: Preface. 1. Solar Magnetism -- an Overview. 2. Theory of Polarized Radiation. 3. Interaction of Matter with Radiation. 4. Radiative Transfer without Scattering. 5. Classical Scattering and the Hanle Effect. 6. Non-LTE Radiative Transfer: Phenomenological Treatment. 7. Introduction to Quantum Field Theory of Polarized Radiative Transfer. 8. Multi-Level Radiative Transfer with Coherence Effects. 9. Rayleigh and Raman Scattering. 10. Collisions, Partial Redistribution, and Turbulent Magnetic Fields. 11. Solutions of the Polarized Transfer Equation. 12. Diagnostics of Small-Scale Magnetic Fields. 13. Instrumentation for Solar Polarimetry. References. Symbol Index. Subject Index.

Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements

Abstract: Ground-based measurements of the solar transmission and sky radiance in a horizontal plane through the Sun are taken in several geographical regions and aerosol types: dust in a desert transition zone in Israel, sulfate particles in Eastern and Western Europe, tropical aerosol in Brazil, and mixed continental/maritime aerosol in California. Stratospheric aerosol was introduced after the eruption of Mount Pinatubo in June 1991. Therefore measurements taken before the eruption are used to analyze the properties of tropospheric aerosol; measurements from 1992 are also used to detect the particle size and concentration of stratospheric aerosol. The measurements are used to retrieve the size distribution and the scattering phase function at large scattering angles of the undisturbed aerosol particles. The retrieved properties represent an average on the entire atmospheric column. A comparison between the retrieved phase function for a scattering angle of 120 deg, with phase function predicted from the retrieved size distribution, is used to test the assumption of particle homogeneity and sphericity in radiative transfer models (Mie theory). The effect was found to be small (20% +/- 15%). For the stratospheric aerosol (sulfates), as expected, the phase function was very well predicted using the Mie theory. A model with a power law distribution, based on the spectral dependence of the optical thickness, alpha, cannot estimate accurately the phase function (up to 50% error for lambda = 0.87 microns). Before the Pinatubo eruption the ratio between the volumes of sulfate and coarse particles was very well correlated with alpha. The Pinatubo stratospheric aerosol destroyed this correlation. The aerosol optical properties are compared with analysis of the size, shape, and composition of the individual particles by electron microscopy of in situ samples. The measured volume size distribution before the injection of stratospheric aerosol consistently show two modes, sulfate particles with r(sub m) less than 0.2 microns and coarse paritcles with r(sub m) greater than 0.7 microns. The 'window' in the tropospheric aerosol in this radius range was used to observe a stable stratospheric aerosol in 1992, with r(sub m) approximately 0.5 microns. A combination of such optical thickness and sky measurements can be used to assess the direct forcing and the climatic impact of aerosol. Systematic inversion for the key aerosol types (sulfates, smoke, dust, and maritime aerosol) of the size distribution and phase function can give the relationship between the aerosol physical and optical properties that can be used to compute the radiative forcing. This forcing can be validated in dedicated field experiments.

Concentrations of chlorophyll, suspended matter, and gelbstoff in case II waters derived from satellite coastal zone color scanner data with inverse modeling methods

Abstract: Color ratio techniques used to derive chlorophyll concentrations from radiance data of the coastal zone color scanner (CZCS) fail in areas with high concentrations of suspended matter and gelbstoff (optically defined as case II water). In order to take into account all water constituents which modify the backscattered radiation field as well as the aerosol path radiance, an inverse modeling technique based on a two-flow radiative transfer approximation and a simplex optimization procedure has been developed. It uses simultaneously the radiances of the first four CZCS spectral channels and minimizes the χ2 difference between the modeled and CZCS-derived “Rayleigh-corrected radiances.” The two-flow model is calibrated with a set of radiance data which was simulated with a matrix-operator radiative transfer model. In a first test, the inverse modeling procedure has been used to produce maps of the quantitative distributions of phytoplankton chlorophyll, suspended matter (dry weight), and gelbstoff; aerosol path radiance; and signal depth of the North Sea. By including the aerosol path radiance as a variable, the procedure implies the atmospheric correction. A map of the residual χ2 values indicates the success of the retrieval for each of the pixels.

Radiative transfer in nonuniformly refracting layered media: atmosphere–ocean system

Abstract: We have applied the discrete-ordinate method to solve the radiative-transfer problem pertaining to a system consisting of two strata with different indices of refraction. The refraction and reflection at the interface are taken into account. The relevant changes (as compared with the standard problem with a constant index of refraction throughout the medium) in formulation and solution of the radiative-transfer equation, including the proper application of interface and boundary conditions, are described. Appropriate quadrature points (streams) and weights are chosen for the interface-continuity relations. Examples of radiative transfer in the coupled atmosphere-ocean system are provided. To take into account the region of total reflection in the ocean, additional angular quadrature points are required, compared with those used in the atmosphere and in the refractive region of the ocean that communicates directly with the atmosphere. To verify the model we have tested for energy conservation. We also discuss the effect of the number of streams assigned to the refractive region and the total reflecting region on the convergence. Our results show that the change in the index of refraction between the two strata significantly affects the radiation field. The radiative-transfer model we present is designed for application to the atmosphere-ocean system, but it can be applied to other systems that need to consider the change in the index of refraction between two strata.

The Tropical Water and Energy Cycles in a Cumulus Ensemble Model. Part I: Equilibrium Climate

Abstract: A cumulus ensemble model is used to study the tropical water and energy cycles and their role in the climate system. The model includes cloud dynamics, radiative processes, and microphysics that incorporate all important production and conversion processes among water vapor and five species of hydrometeors. Radiative transfer in clouds is parameterized based on cloud contents and size distributions of each bulk hydrometeor. Several model integrations have been carried out under a variety of imposed boundary and large-scale conditions. In Part I of this paper, the primary focus is on the water and heat budgets of the control experiment, which is designed to simulate the convective–radiative equilibrium response of the model to an imposed vertical velocity and a fixed sea surface temperature at 28°C. The simulated atmosphere is conditionally unstable below the freezing level and close to neutral above the freezing level. The equilibrium water budget shows that the total moisture source, Ms, which i...

Studies of the radiative properties of ice and mixed-phase clouds

Abstract: Radiative parametrizations for both ice and water clouds are developed in terms of liquid/ice water content, based on Mie scattering theory. For ice crystals the application of Mie theory is guided by the hexagonal-crystal/equivalent-spheres comparison of Takano and Liou. These parametrizations are extensively tested against measurements from aircraft and are shown to perform satisfactorily, although corrections for unobserved small crystals and the effect of crystal shape are large and not currently well defined. The parametrizations are then used to investigate the effect of mixed-phase clouds on radiative transfer. It is found that, because the radiative properties of ice crystals and liquid droplets are significantly different, the radiative properties of mixed-phase clouds cannot be simulated successfully if the ice in clouds is converted into liquid water. Both the albedo and the rate of change of albedo with ice fraction are significantly dependent on the method by which the phases are mixed; these factors may be of especial importance in climate-sensitivity experiments that incorporate mixed-phase clouds. The presence of ice in clouds below the cirrus level is often ignored in climate-model and radiation-budget studies. The calculations presented here indicate that this neglect may lead to a serious bias in cloud albedo for a given path of condensed water.

Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part I: Theoretical characteristics of normalized polarization and scattering indices

Abstract: Microwave rain rate retrieval algorithms have most often been formulated in terms of the raw brightness temperatures observed by one or more channels of a satellite radiometer. Taken individually, single-channel brightness temperatures generally represent a near-arbitrary combination of positive contributions due to liquid water emission and negative contributions due to scattering by ice and/or visibility of the radiometrically cold ocean surface. Unfortunately, for a given rain rate, emission by liquid water below the freezing level and scattering by ice particles above the freezing level are rather loosely coupled in both a physical and statistical sense. Furthermore, microwave brightness temperatures may vary significantly (∼30–70 K) in response to geophysical parameters other than liquid water and precipitation. Because of these complications, physical algorithms which attempt to directly invert observed brightness temperatures have typically relied on the iterative adjustment of detailed microphysical profiles or cloud models, guided by explicit forward microwave radiative transfer calculations.

A Model Predicting the Evolution of Ice Particle Size Spectra and Radiative Properties of Cirrus Clouds. Part II: Dependence of Absorption and Extinction on Ice Crystal Morphology.

Abstract: This study builds upon the microphysical modeling described in Part 1 by deriving formulations for the extinction and absorption coefficients in terms of the size distribution parameters predicted from the micro-physical model. The optical depth and single scatter albedo of a cirrus cloud can then be determined, which, along with the asymmetry parameter, are the input parameters needed by cloud radiation models. Through the use of anomalous diffraction theory, analytical expressions were developed describing the absorption and extinction coefficients and the single scatter albedo as functions of size distribution parameters, ice crystal shapes (or habits), wavelength, and refractive index. The extinction coefficient was formulated in terms of the projected area of the size distribution, while the absorption coefficient was formulated in terms of both the projected area and mass of the size distribution. These properties were formulated as explicit functions of ice crystal geometry and were not based on an 'effective radius.' Based on simulations of the second cirrus case study described in Part 1, absorption coefficients predicted in the near infrared for hexagonal columns and rosettes were up to 47% and 71% lower, respectively, than absorption coefficients predicted by using equivalent area spheres. This resulted in single scatter albedos in the near-infrared that were considerably greater than those predicted by the equivalent area sphere method. Reflectances in this region should therefore be underestimated using the equivalent area sphere approach. Cloud optical depth was found to depend on ice crystal habit. When the simulated cirrus cloud contained only bullet rosettes, the optical depth was 142% greater than when the cloud contained only hexagonal columns. This increase produced a doubling in cloud albedo. In the near-infrared (IR), the single scatter albedo also exhibited a significant dependence on ice crystal habit. More research is needed on the geometrical properties of ice crystals before the influence of ice crystal shape on cirrus radiative properties can be adequately understood. This study provides a way of coupling the radiative properties of absorption, extinction, and single scatter albedo to the microphysical properties of cirrus clouds. The dependence of extinction and absorption on ice crystal shape was not just due to geometrical differences between crystal types, but was also due to the effect these differences had on the evolution of ice particle size spectra. The ice particle growth model in Part 1 and the radiative properties treated here are based on analytical formulations, and thus represent a computationally efficient means of modeling the microphysical and radiative properties of cirrus clouds.

Heat Feedback to the Fuel Surface in Pool Fires

Abstract: A series of measurements designed to investigate the heat feedback in pool fires burning liquid fuels are reported. Such measurements are essential for the development and validation of detailed models which predict the burning rate of liquid hydrocarbons and solid polymers. The radial variation of the local radiative and local net heat flux incident on the surface of 0.30 m diameter pool fires were measured. A water-cooled, nitrogen purged, narrow view-angle gauge was developed to measure the radiative flux incident on the fuel surface. Measurements of the mass burning rate in a burner composed of annular rings was used to estimate the local heat feedback. A number of different fuels were studied, yielding flames with a wide range of heat release rates and luminosities. Consideration of the heat balance for a control volume enclosing the liquid PPOI indicated that radiation was an important component of the heat feedback for non-luminous fires and a dominant component in luminous fires.